Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 142, pp. 1-8.
Title: Irregular oblique derivative problems for second-order
nonlinear elliptic equations on infinite domains
Author: Guo Chun Wen (Peking Univ., Beijing, China)
Abstract:
In this article, we study irregular oblique derivative
boundary-value problems for nonlinear elliptic equations of
second order in an infinite domain. We first provide the formulation
of the above boundary-value problem and obtain a representation theorem.
Then we give a priori estimates of solutions by using the reduction
to absurdity and the uniqueness of solutions. Finally by the above
estimates and the Leray-Schauder theorem, the existence of solutions
is proved.
Submitted July 20, 2012. Published August 20, 2012.
Math Subject Classifications: 35J65, 35J25, 35J15.
Key Words: Irregular oblique derivative problem; nonlinear elliptic equations;
infinite domains.